Michigan Mathematical Journal

Hyperbolicity Notions for Varieties Defined over a Non-Archimedean Field

R. Rodríguez Vázquez

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Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semidistance dCK, which he introduced for analytic spaces defined over a non-Archimedean metrized field k. We prove various characterizations of smooth projective varieties for which dCK is an actual distance.

Secondly, we explore several notions of hyperbolicity for a smooth algebraic curve X defined over k. We prove a non-Archimedean analogue of the equivalence between having a negative Euler characteristic and the normality of certain families of analytic maps taking values in X.

Article information

Michigan Math. J., Volume 69, Issue 1 (2020), 41-78.

Received: 3 January 2018
Revised: 29 August 2018
First available in Project Euclid: 21 November 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
Secondary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions


Rodríguez Vázquez, R. Hyperbolicity Notions for Varieties Defined over a Non-Archimedean Field. Michigan Math. J. 69 (2020), no. 1, 41--78. doi:10.1307/mmj/1574326880. https://projecteuclid.org/euclid.mmj/1574326880

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